Derivatives option Greeks gamma short gamma gamma scalping expiry risk

Gamma (options)

From WebNotes, a public knowledge base. Last updated 21 June 2026. Reading time ~12 min.

Key facts

What it measures	The change in an option's delta for a Re 1 change in the underlying; it is the second-order sensitivity, the rate of change of delta
Sign	Always positive for both calls and puts; a long option is long gamma, a short option is short gamma
Where it peaks	Highest for at-the-money options and rises sharply in the final days and hours before expiry
Where it is lowest	Deep in-the-money and deep out-of-the-money options carry low gamma
Why sellers fear it	A short option is short gamma; a sharp move makes delta turn rapidly against the writer, the central risk of premium selling
Where to read it on Kite	Option chain, Greeks tab; the value is per unit of the underlying, so multiply by the lot size

Gamma is the second-order option Greek that measures how fast an option’s delta changes when the underlying moves by one rupee, holding time and volatility constant. Where delta tells you the current directional exposure, gamma tells you how quickly that exposure will shift, so a call with delta 0.50 and gamma 0.02 sees its delta rise to about 0.52 after a one-point rise in the underlying. Gamma is always positive for a bought option, peaks for at-the-money strikes, and rises sharply in the final days before expiry.

Gamma is the Greek that turns a comfortable short-premium position into a loss faster than the trader expects. A position that is delta-neutral at 9.30 in the morning can carry a large losing delta by mid-afternoon if the underlying moves two per cent, purely because gamma kept reshaping the delta. This article defines gamma precisely, sets out where it is large and small, explains the short-gamma risk that sits at the centre of option writing, and covers gamma scalping, the long-gamma strategy that monetises the same effect from the other side. For the first-order Greek it acts on, see delta ; for the time-decay cost that pays the short-gamma writer, see theta .

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Definition and units

Gamma is the partial derivative of delta with respect to the underlying price, which makes it the second derivative of the option premium. It answers a different question from delta: not how much the premium moves, but how much the rate of movement itself changes. A long Nifty call showing delta 0.40 and gamma 0.03 will, after a one-point rise in the Nifty 50, carry a delta of about 0.43; after a one-point fall, about 0.37. Gamma is the engine that drives delta around.

The Kite Greeks tab reports gamma per unit of the underlying, in the same per-share convention as delta. Because index option deltas span a range of only 1.0 from deep out-of-the-money to deep in-the-money, gamma values look small in absolute terms, often a few hundredths or thousandths, but their effect compounds across a large move and across a full lot. Multiplying the per-unit gamma by the lot size and by the size of the underlying move gives the rupee change in position delta, which is the figure that matters for risk.

Gamma is always positive for a single bought option, call or put. The sign a trader carries depends on direction: a long option gives positive position gamma, a short option gives negative position gamma. The Varsity gamma chapters state the rule plainly, that buying options makes you long gamma and selling options makes you short gamma, and that a large gamma translates into large directional risk for the writer.

Where gamma is large and small

Gamma is not uniform across strikes. It concentrates around the money and thins out at the extremes, and it changes shape as expiry approaches.

Option	Approximate gamma	Why
Deep in-the-money	Low	Delta is already near 1 or -1 and barely moves
At-the-money	Highest	Delta swings fastest as the underlying crosses the strike
Deep out-of-the-money	Low	Delta is already near 0 and barely moves

The at-the-money peak follows directly from how delta behaves. At the strike, a small move in the underlying flips the option between gaining and losing intrinsic value, so its delta changes fastest there. Deep in-the-money, delta already sits near 1 and a further move changes it little; deep out-of-the-money, delta sits near 0 and a small move barely lifts it. The Varsity material adds that with ample time to expiry, all three of in-the-money, at-the-money and out-of-the-money carry fairly low and similar gamma, and the gap between them widens only in the back half of the contract’s life.

The relationship to gamma’s neighbours is worth holding together. Gamma is highest exactly where delta is most uncertain and where vega is also largest, at the money. The Greeks do not act in isolation, and Varsity stresses reading the premium as a function of all of them rather than any one in a silo. For how moneyness maps to delta and premium across the chain, see moneyness: in-the-money, at-the-money, out-of-the-money .

Why gamma spikes near expiry

The single most dangerous property of gamma is its behaviour in the final hours of a contract. As expiry nears, an at-the-money option’s delta must resolve to either 1 (it finishes in-the-money) or 0 (it finishes worthless), and there is almost no time left for the outcome to change. That forces the delta to swing between near 0 and near 1 over a very small price range as the underlying hovers around the strike, which is the same as saying gamma has become large.

The practical effect on a weekly contract is sharp. A near-at-the-money option that looked harmless in the morning can shift from nearly worthless to worth hundreds of rupees per unit, or the reverse, on a one per cent move in the last hour of expiry day. This is why expiry-day positions demand attention disproportionate to their premium; see expiry-day options trading for the mechanics and stock-option restrictions near expiry for the contract-level constraints. The SEBI index-derivatives package that took effect from 20 November 2024 layered extra expiry-day margin add-ons on top of this risk, partly in response to the expiry-day churn that gamma drives; see the weekly-expiry contraction of November 2024 and the SEBI F&O entry-barrier rules of 2024 .

Short-gamma risk for option sellers

A short option carries negative gamma, and negative gamma is the structural risk of premium selling. The mechanism is direct: as the underlying moves against a short position, gamma makes the position’s delta turn against the writer faster the further it moves. A short straddle or short strangle that was set up delta-neutral develops a large negative delta on a strong upside move and a large positive delta on a strong downside move, losing on either, and the loss accelerates rather than running at a steady rate.

Consider a writer short an at-the-money index straddle, delta-neutral at outset. A two to three per cent intraday move pushes the position’s delta well away from zero, and because gamma is highest at the money and near expiry, the delta keeps accelerating in the losing direction as the move extends. The writer who does nothing watches a small loss become a large one; the writer who delta-hedges is forced to buy the underlying after it has already risen and sell it after it has already fallen, paying for each rehedge, which is the cost that the collected premium is meant to cover. Short gamma and short vega usually travel together on a premium-selling book, so a sharp move that spikes both is doubly punishing.

The margin system prices this risk. The exchange’s SPAN-plus-exposure framework scenarios a range of underlying moves and charges margin against the worst, which for a short option is driven by gamma; see SPAN margin on Zerodha , exposure margin on Zerodha and naked option-selling margin on Zerodha for how the requirement is built. Varsity’s standing advice is to avoid shorting options with large gamma, which in practice means avoiding selling at-the-money strikes close to expiry without a tight risk plan.

Gamma scalping

Gamma scalping is the long-gamma strategy that monetises the same effect from the buyer’s side. A trader holds options, which gives positive gamma, and delta-hedges with the underlying or its future. As the underlying moves, positive gamma accumulates delta in the profitable direction, and the trader rebalances the hedge: selling the underlying after a rise and buying it back after a fall. Each rehedge locks in a small gain, buying low and selling high, and the sequence of small gains is the scalp.

The catch is that long gamma is paid for with long theta . The options that supply the positive gamma decay every day, so the gamma scalper needs the underlying to move enough, and oscillate enough, for the rehedging gains to exceed the daily time decay. In a quiet, trendless market the theta bleed wins and the scalper loses; in a choppy, high-realised-volatility market the scalp wins. This is why gamma scalping is fundamentally a bet that realised volatility will exceed the implied volatility paid for the options, the same trade expressed through vega and implied volatility . At retail scale the strategy is constrained by lot sizes, which make the hedge approximate, and by transaction costs on every rebalance; see Zerodha F&O charges .

Gamma, theta and the volatility trade

Gamma never sits alone on a position. A long option that carries positive gamma also carries negative theta , and the relationship between the two defines whether holding the option pays. The gamma supplies the convexity that lets a delta-hedged holder rebalance profitably, while theta charges a daily rent for that convexity. The position turns a profit only when the gains harvested from rebalancing the positive gamma exceed the theta paid each day, which happens when the underlying actually moves and oscillates rather than drifting quietly.

That is why gamma is, at bottom, a bet on realised volatility against the implied volatility paid for the option. A long-gamma, long-theta position wins when realised volatility runs above the implied volatility embedded in the premium, and loses when the market is calmer than the premium priced; the short-gamma, long-theta writer takes the opposite side of the same bet. The Varsity Greek-interactions material makes the same point from the premium side: a high gamma does little if the underlying does not move, just as a high vega does little if implied volatility does not change, so the position must be read as the product of all the Greeks together. For the implied-volatility input that sets the rent, see implied volatility and India VIX ; for how the same tradeoff drives strike choice, see strike selection on the option chain .

A practical consequence for an Indian retail book is that gamma is hardest to manage exactly where it is largest and cheapest to acquire: at-the-money weekly options in the final two or three sessions. Those contracts offer the most convexity per rupee of premium, which draws buyers, and the most decay per day, which draws writers, so they concentrate both sides of the gamma trade into the riskiest window of the contract’s life. The November 2024 expiry-day margin add-ons sit precisely on that window; see the weekly-expiry contraction of November 2024 .

Gamma on the Kite option chain

In Kite, the Greeks tab of the option chain shows gamma for every call and put at every listed strike, computed from the Black-Scholes-Merton model using the mid-market implied volatility. The figure is per unit of the underlying, so multiply by the lot size for the position figure. For European-style index options the model fits well; for American-style single-stock options the displayed gamma is an approximation, useful for comparing strikes but less precise for deep-in-the-money or very short-dated contracts. Because gamma is derived from the same implied volatility as the other Greeks, an illiquid strike with a wide bid-ask spread produces a gamma that should be read as indicative only. For where to find the tab, see how to read option Greeks on Kite and how to use the options chain on Kite ; for net gamma across a multi-leg book, see how to build an options strategy on Sensibull .

External references

References

Black, F. and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637 to 654.
Hull, J.C. (2021). Options, Futures, and Other Derivatives (11th ed.). Pearson, chapters on the Greek letters.
Zerodha Varsity, Option Theory for Professional Trading, gamma and Greek-interaction chapters (as of June 2026).
SEBI circular on measures to strengthen index derivatives, effective from 20 November 2024 (expiry-day margin add-ons).
SEBI, Analysis of Profit and Loss of Individual Traders Dealing in Equity F&O Segment, January 2023 and the September 2024 update.

Frequently asked questions

What is gamma in options?

Gamma is the rate at which an option’s delta changes for a Re 1 move in the underlying. If a call has delta 0.50 and gamma 0.02, a Re 1 rise lifts delta to about 0.52. Gamma is the second-order Greek that governs how fast directional exposure builds.

Why is gamma highest at-the-money?

At the money a small move in the underlying flips the option between gaining and losing intrinsic value, so its delta changes fastest there. Deep in-the-money and deep out-of-the-money options have delta near 1 or 0 that barely moves, so their gamma is low.

Why do option sellers fear gamma?

A short option is short gamma. On a sharp move the position’s delta turns against the writer rapidly, so a position that looked delta-neutral can develop a large losing delta within minutes. This short-gamma risk is the main danger of premium selling, worst near expiry.

What is gamma scalping?

Gamma scalping is a long-gamma strategy: a trader holds options and delta-hedges with the underlying, then rebalances as the move accumulates delta. Long gamma forces buying low and selling high on each rehedge, capturing small gains that offset the theta paid to hold the options.

Why does gamma spike near expiry?

Near expiry an at-the-money option’s delta swings between near 0 and near 1 over a tiny price range, because there is little time left for the outcome to change. That makes delta hypersensitive to the underlying, so gamma rises sharply, fastest on expiry day.

Is gamma always positive?

For a single bought option, yes, for both calls and puts. The sign you carry depends on direction: a long option gives you positive position gamma, a short option gives you negative position gamma. A book’s net gamma can be positive or negative depending on its legs.

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Last reviewed: 21 June 2026
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